A rope of 18m is used to form
a sector of a circle of radius 3.5m,
on a school playing field. What is
the size of the angle of the sector,
correct to the nearest degree.
A. 33
B. 40
C. 90
D. 180
To find the size of the angle of the sector, we need to find the arc length of the sector and then use the formula for arc length to find the angle.
The arc length of the sector is given by the formula:
arc length = (angle/360) * 2πr
Where angle is the size of the angle of the sector in degrees, and r is the radius of the sector.
We can rearrange this formula to solve for the angle:
angle = (arc length / (2πr)) * 360
In this case, the arc length is given as 18m and the radius is given as 3.5m. Substituting these values into the formula, we get:
angle = (18 / (2π(3.5))) * 360
angle ≈ 32.57 degrees
Rounding to the nearest degree, the size of the angle of the sector is 33 degrees. Therefore, the correct answer is A. 33.
To find the size of the angle of the sector, we can use the formula:
angle = (arc length / circumference) * 360 degrees
Given that the rope forms a sector of a circle with a radius of 3.5m, we can calculate the circumference of the circle as:
circumference = 2 * π * radius
Substituting the given value, we get:
circumference = 2 * π * 3.5m
= 7π m
Now we can calculate the arc length using the given rope length of 18m:
arc length = 18m
Substituting these values into the formula for the angle:
angle = (arc length / circumference) * 360 degrees
= (18m / (7π m)) * 360 degrees
≈ 82.03 degrees
Therefore, the size of the angle of the sector is approximately 82 degrees.
None of the given options (A, B, C, D) matches the answer.